Heavily damaged Fiterman Hall — ripped apart by falling debris on 9/11 and filled with toxins — will be razed by the end of October, workers told The Post.

All 16 floors of the CUNY building — formerly a performance hall for Borough of Manhattan Community College where classrooms, offices, a public cafe and gallery spaces will rise — have been detoxed, said Benn Lewis, vice president of Airtek Environmental Corp.

That puts Fiterman many months ahead of the nearby Deutsche Bank building, another 9/11-scarred edifice that won’t be demolished until early next year.